Atlas3,149 of 3,942

Choreography CH.399

From Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2023)

Choreography CH.399 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 784.99 time units, published by Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2023). All three bodies follow one closed curve, each a third of a period behind the next. Every one here is linearly stable. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.366 of each other at a top speed of 1.74, line up 906 times a period, and the computed loop closes to 2.1×10⁻²⁷.

Measured over one period

Period: 784.9887143
Masses: 1 : 1 : 1
Energy: -1.46702
Angular momentum: 0
Closest approach: 0.3660
Top speed: 1.736
Path length: 2175.9
Alignments per period: 906
Topology: (abAB)¹⁵¹ (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 2.1×10⁻²⁷

Neighbours on the map

All Choreographies, the families of periodic three-body orbits, or the atlas map.